where the LECs \(g^{\pi \pi }_{1,4,5}\)  are known from lattice QCD [1]}, [2]}
and scale as \(g_1^{\pi \pi } \sim \mathcal {O}(1)\)  and \(g_{4,5}^{\pi \pi } \sim \mathcal {O}(\Lambda _\chi ^2)\) .
From this scaling it is clear that the dominant contribution to the two-pion matrix element is proportional to the combination
\(g_{LR}^{\pi \pi } \equiv (1/2) (g_4^{\pi \pi } - 3 g_5^{\pi \pi })\) .
